This talk is based on [1,2,3]. Until less than 10 years ago, post-Newtonian (pN) analysis was the only possible systematic method for obtaining gravitational waveforms corresponding to binary inspiral. However, these were cut-off before the merger, until the recent availability of direct results from numerical relativity computations, which could include the complete merger and ring-down phase of the orbital evolution. Unfortunately these calculations are not yet of sufficient precision to strenuously test pN methods intrinsically. By contrast, the gravitational self-force approach has become capable of advancing to extremely high precision, and of thereby testing most of the various techniques used in pN calculations. Although restricted to the extreme-mass-ratio limit, self-force calculations are now able to verify both the methods and results of pN work, and even of extending it. In fact, as will be demonstrated, they now have high enough precision to be able to determine new coefficients analytically.